Rare-event asymptotics and estimation for dependent random sums – an exit talk, with applications to finance and insurance

Speaker: Mr Patrick Laub, UQ

Modern financers and insurers need to understand the risk they own in their portfolios, and to estimate the chance of a catastrophic loss or bankruptcy. Even with the most basic models (such as those of Black & Scholes or of Cramér & Lundberg) simple quantities such as quantiles are impossible to calculate directly. In my PhD, I have worked on density and Laplace transform approximation for the distribution of the sum of lognormals. Recently, with Pierre-Olivier Goffard, we have generalised the density approximation method (which relies on an orthogonal polynomial expansion) to general random sums. I'll outline the numerical aspects of the work, which includes quasi-Monte Carlo integration with importance sampling, and symbolic differentiation within Mathematica’s infinite precision algebra. The papers covered are available on Patrick's website.